It is possible to regard the history of the foundation of mathematics as a progressive enlarging of the mathematical universe to include more and more infinities. The Greek word for infinity was apeiron, which literally means unbounded, but can also mean infinite, indefinite, or undefined. Apeiron was a negative, even pejorative word. The original chaos out of which the world was formed was apeiron. An arbitrary crooked line was apeiron. A dirty crumpled handkerchief was apeiron. Thus, apeiron need not only mean infinitely large, but can also mean totally disordered, infinitely complex, subject to no finite determination. In Aristotle’s words, “. . . being infinite is a privation, not a perfection but the absence of limit. . .”
– Rudy Rucker
Cosmic Flotsam 